Price Impacts of Imperfect Collateralization (Revised as CARF-F-375 in November 2015)

Abstract

This paper studies impacts of imperfect collateralization on derivatives values. Firstly, we present a general framework for the analysis in a multi-dimensional diffusion setting, and then calclate pre-default values of forwards and options for the numerical experiments. In particular, we investigate no collateral posting and timelagged collateral posting cases under a stochastic volatility model for the underlying asset prices and stochastic interest and hazard rate models for the risk-free rate and default intensities. We also derive an approximation for the density function of the CVA (Credit Value Adjustment) in the valuation of forward contract with bilateral counter party risk. Moreover, we allow a stochastic collateral asset value to depend not only on the underlying contract values, but also on other asset prices such as a currency different from the payment currency of the underlying contract. Finally, we also examine the effect of correlations on basket option values with stochastic volatility and stochastic hazard rate models.